Biophysical theory regards the electrophysiological interaction between passive and active patches of nerve membrane as functionally significant. Important examples are interactions such as an active soma attached to a dendritic tree, myelinated nerves, and the possibility of dendrictic spines with excitable spine head membranes. The aim of this project is to explore, using mathematical modeling, analysis, and numerical computation the functional implications of these interactions. To aid this study we also introduce a new bifurcation analysis that is applicable to a general class of chemical and biochemical models, and exploit the multiple-scale perturbation method to study the response of the FitzHughNagumo system when forced by a periodic applied current source.